by jsendak | Jan 7, 2026 | GR & QC Articles
arXiv:2601.02416v1 Announce Type: new
Abstract: We present a complete analytic and semi-analytic study of gravitational collapse and primordial black hole (PBH) formation in the quadratic $f(R)$ model $f(R)=R+alpha R^2$. We first derive the perturbative expansion around General Relativity (GR), working to first order in the small parameter $alpha$. For a collapsing flat FLRW dust interior we compute the explicit first-order corrections to the scale factor, the stellar radius, and the horizon formation time. We then use these results to obtain the shift in the PBH formation threshold $delta_c$. The perturbative effect is small for PBHs forming in the deep radiation era, but becomes important when the background curvature is high. To access this early regime we reformulate the theory in the Einstein frame, where the model becomes GR plus the scalaron field $phi$ with the Starobinsky potential. We provide the complete ODE system governing both the cosmological background and the evolution of an overdense closed FLRW patch. This system can be numerically integrated to obtain the critical overdensity $delta_c(k)$ for PBH formation near the end of inflation.
Conclusions
The study of gravitational collapse and primordial black hole formation in the quadratic $f(R)$ model $f(R)=R+alpha R^2$ provides valuable insights into the early universe dynamics. The perturbative expansion around General Relativity allows for a detailed analysis of corrections to scale factors, stellar radii, and horizon formation times. The shift in the PBH formation threshold $delta_c$ is found to be significant in high-curvature backgrounds, highlighting the importance of considering alternative gravity models in extreme conditions.
Reformulating the theory in the Einstein frame offers a new perspective, transforming the model into GR plus the scalaron field $phi$ with the Starobinsky potential. By solving the complete ODE system governing cosmological backgrounds and the evolution of overdense closed FLRW patches, critical overdensities $delta_c(k)$ for PBH formation near the end of inflation can be obtained.
Future Roadmap
Challenges:
- Validation of perturbative results against simulations and observational data.
- Understanding the implications of high-curvature backgrounds on early universe dynamics.
- Numerical integration of the ODE system for accurate determination of critical overdensities.
Opportunities:
- Exploration of the role of alternative gravity models in cosmological evolution.
- Investigation of PBH formation in the early universe as a probe of fundamental physics.
- Potential implications for the nature of dark matter and the cosmological constant.
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by jsendak | Jan 7, 2026 | Cosmology & Computing
Black holes are some of the most mysterious and fascinating objects in the universe. These massive objects, formed from the remnants of collapsed stars, have such strong gravitational pull that not even light can escape their grasp. At the center of a black hole lies a singularity, a point of infinite density where the laws of physics as we know them break down.
The concept of a singularity can be difficult to grasp, as it defies our understanding of the universe. In simple terms, a singularity is a point where the gravitational pull becomes infinitely strong, causing matter to be crushed to an infinitely small size. This point of infinite density is surrounded by an event horizon, the boundary beyond which nothing can escape the black hole’s gravitational pull.
The singularity is often referred to as the “point of no return” because once an object crosses the event horizon, it is inevitably pulled towards the singularity and crushed into oblivion. This phenomenon is known as spaghettification, where the intense gravitational forces stretch and distort any object that gets too close to the singularity.
The existence of singularities in black holes raises many questions about the nature of the universe and the laws of physics. According to Einstein’s theory of general relativity, singularities are a natural consequence of the extreme conditions within a black hole. However, at the singularity, the laws of physics as we know them break down, leading to a paradox known as the black hole information paradox.
The black hole information paradox suggests that information about the matter that falls into a black hole is lost forever once it reaches the singularity. This contradicts the principle of quantum mechanics, which states that information cannot be destroyed. Scientists are still grappling with this paradox and trying to reconcile the conflicting theories of general relativity and quantum mechanics.
Despite the mysteries surrounding black hole singularities, they play a crucial role in shaping the universe. Black holes are thought to play a key role in the formation of galaxies and the evolution of the cosmos. By studying black holes and their singularities, scientists hope to gain a deeper understanding of the fundamental laws of physics and the nature of the universe.
In conclusion, black hole singularities represent the point of no return, where the laws of physics as we know them break down and matter is crushed into oblivion. These enigmatic objects challenge our understanding of the universe and raise profound questions about the nature of reality. By delving into the mysteries of black holes, scientists are pushing the boundaries of our knowledge and unlocking the secrets of the cosmos.
by jsendak | Jan 4, 2026 | Cosmology & Computing
Black holes are one of the most mysterious and fascinating objects in the universe. These massive cosmic entities have such strong gravitational pulls that not even light can escape from them, making them invisible to the naked eye. However, one of the most intriguing aspects of black holes is their singularities – the point at which the laws of physics break down and our understanding of the universe is put to the test.
A singularity is a point in space where the gravitational pull becomes infinitely strong, causing matter to be crushed into an infinitely small and dense point. In the case of a black hole, this singularity is located at the center, or “heart,” of the black hole. It is a point of no return, where the laws of physics as we know them cease to exist.
The concept of a singularity was first proposed by physicist Albert Einstein in his theory of general relativity. According to this theory, when a massive star collapses under its own gravity, it forms a black hole with a singularity at its center. At this point, the laws of physics as we know them break down, and our understanding of the universe is put to the test.
One of the most intriguing aspects of black hole singularities is the fact that they are hidden from view. Because light cannot escape from a black hole, we cannot directly observe the singularity at its center. Instead, we can only infer its existence based on the behavior of matter and radiation around the black hole.
Despite the mystery surrounding black hole singularities, scientists have made significant progress in understanding them. One of the most important developments in this field was the discovery of the black hole information paradox, which states that information that falls into a black hole is lost forever. This paradox has led to intense debate among physicists and has challenged our understanding of the fundamental laws of physics.
Another important aspect of black hole singularities is their connection to the concept of wormholes – hypothetical tunnels in spacetime that could potentially allow for faster-than-light travel. Some scientists believe that black hole singularities could be connected to wormholes, providing a gateway to other parts of the universe.
In conclusion, black hole singularities are one of the most intriguing and mysterious phenomena in the universe. They represent the point of no return, where the laws of physics as we know them break down and our understanding of the universe is put to the test. While much remains unknown about black hole singularities, scientists continue to study them in the hopes of unlocking the secrets of the universe.
by jsendak | Dec 6, 2025 | Cosmology & Computing
Black holes are some of the most mysterious and fascinating objects in the universe. These massive structures, formed from the remnants of collapsed stars, possess such strong gravitational forces that not even light can escape their grasp. At the heart of every black hole lies a singularity, a point of infinite density where the laws of physics as we know them break down. Understanding the enigmatic nature of black hole singularities is a key area of research in astrophysics and cosmology.
The concept of a singularity was first introduced by physicist Albert Einstein in his theory of general relativity. According to this theory, when a massive star collapses under its own gravity, it forms a singularity at its center. This singularity is a point of infinite density and zero volume, where the laws of physics as we know them cease to apply. The gravitational forces near a singularity are so strong that they warp space and time, creating a region of spacetime known as a black hole.
One of the most puzzling aspects of black hole singularities is the fact that they are hidden from view. Because light cannot escape from a black hole, we cannot directly observe the singularity at its center. This makes it difficult for scientists to study and understand the properties of black hole singularities. However, through mathematical models and computer simulations, researchers have been able to gain some insight into the nature of these enigmatic objects.
One of the most intriguing aspects of black hole singularities is the concept of the event horizon. This is the point of no return beyond which nothing can escape the gravitational pull of a black hole. The event horizon acts as a barrier that prevents any information from inside the black hole from reaching the outside world. This has led to the famous “information paradox,” which questions what happens to the information of matter that falls into a black hole.
Another mystery surrounding black hole singularities is the issue of what lies beyond the event horizon. Some scientists believe that black holes may contain hidden universes or wormholes that connect different regions of spacetime. Others speculate that black hole singularities may be portals to other dimensions or alternate realities. These ideas are purely speculative and have not been proven, but they highlight the enigmatic and mysterious nature of black hole singularities.
Despite the many unanswered questions surrounding black hole singularities, scientists continue to study these objects in the hopes of unlocking their secrets. By combining theoretical models with observations from telescopes and other instruments, researchers are gaining a better understanding of the properties and behavior of black holes. The study of black hole singularities is a complex and challenging field, but it holds the potential to revolutionize our understanding of the universe and the fundamental laws of physics.
In conclusion, the enigmatic nature of black hole singularities continues to intrigue and mystify scientists and researchers. These objects represent some of the most extreme and mysterious phenomena in the universe, and studying them is essential for advancing our knowledge of the cosmos. While many questions remain unanswered, the study of black hole singularities is a crucial area of research that has the potential to uncover new insights into the nature of spacetime, gravity, and the fundamental laws of the universe.
by jsendak | Nov 27, 2025 | Cosmology & Computing
The universe is a vast and mysterious place, filled with countless wonders that continue to captivate and intrigue scientists and astronomers alike. Over the years, our understanding of the cosmos has grown exponentially, thanks to advancements in technology and the tireless efforts of researchers around the world. In recent years, cosmologists have made significant breakthroughs in unraveling some of the universe’s most perplexing mysteries, shedding light on the origins and evolution of the cosmos.
One of the most exciting developments in cosmology in recent years is the discovery of dark matter and dark energy. Dark matter is a mysterious substance that makes up about 27% of the universe, yet it does not emit, absorb, or reflect light, making it invisible and undetectable by traditional telescopes. Despite its elusive nature, scientists have been able to infer the existence of dark matter through its gravitational effects on visible matter in the universe. Dark energy, on the other hand, is a mysterious force that is causing the universe to expand at an accelerating rate. Together, dark matter and dark energy make up about 95% of the universe, leaving only 5% for visible matter such as stars, planets, and galaxies.
Another major breakthrough in cosmology is the confirmation of the existence of gravitational waves, ripples in the fabric of spacetime that are produced by cataclysmic events such as the collision of black holes or neutron stars. In 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) made history by detecting gravitational waves for the first time, confirming a key prediction of Albert Einstein’s theory of general relativity. Since then, LIGO and other gravitational wave detectors have detected numerous gravitational wave events, providing astronomers with a new tool to study the universe and explore its most extreme phenomena.
Cosmologists have also made significant progress in understanding the early universe and the processes that led to the formation of galaxies and other cosmic structures. The cosmic microwave background radiation, leftover radiation from the Big Bang, has provided valuable insights into the conditions of the early universe and the seeds of cosmic structure. By studying the cosmic microwave background, scientists have been able to refine our understanding of the age, composition, and geometry of the universe, as well as the processes that gave rise to the first galaxies and stars.
As our understanding of the universe continues to deepen, cosmologists are faced with new questions and challenges that push the boundaries of our knowledge. From the nature of dark matter and dark energy to the search for extraterrestrial life, there is still much to learn and discover about the cosmos. With ongoing advancements in technology and the collaborative efforts of scientists around the world, we can look forward to even more exciting insights and discoveries in the field of cosmology in the years to come.
In conclusion, the mysteries of the universe continue to fascinate and inspire us, driving us to explore the cosmos and unlock its secrets. Through the efforts of dedicated researchers and the power of technology, we are making remarkable progress in unraveling the mysteries of the cosmos and gaining a deeper understanding of our place in the universe. As we continue to push the boundaries of our knowledge, the future of cosmology looks brighter than ever, promising new insights and discoveries that will shape our understanding of the universe for generations to come.
