arXiv subjects

Don N. Page

Publications and source records attributed to Don N. Page.

At least 19 recordsLinked to original sources

arXiv2026

Crudely Estimated Maximum Mass for a Cosmological Black Hole

$N$-body simulations by M.~Milosavljevic and D.~Merritt \cite{Milosavljevic:2001vi} suggest that for supermassive black hole binaries in their expected nearly circular orbits, before gravitational wave emission dominates, the inspiral rate causes the dimensionless orbital relative velocity squared, $(v/c)^2$, to increase nearly linearly with time at a rate that is approximately the inverse of 210 Gyr (about 15 times the present age of the universe), nearly independently of the mass of the binary. This by itself would not lead to coalescence by the present time, but when it is augmented by gravitational radiation, it can lead to coalescence for equal-mass black hole binaries up to about $1.4\times 10^{14} M_\odot$, which might then be conjectured to be a very crude upper limit to the mass of black holes in our universe at the present time. This also suggests that the gravitational wave strain from coalescing supermassive black hole binaries should decrease for wave periods greater than about 100\,000 years.

gr-qc↗

arXiv2026

Two-Point Padé Approximants for the Deflection of Light in the Schwarzschild Black Hole Metric

The deflection angle of a light ray passing the Schwarzschild (spherically symmetric vacuum) black hole was calculated by Charles Galton Darwin in 1959 in terms of the elliptic integral of the first kind. This calculation has been repeated many times and has also been given approximately in terms of elementary functions for impact parameters that either are not too small or are close to the critical impact parameter. Here I present Padé 2-point approximants of order [2,2] (quadratic numerators and denominators), relating the critical impact parameter divided by the actual impact parameter to the exponential of the negative of the deflection angle, that fairly accurately cover the full range of impact parameters greater than the critical impact parameter, which is the case for all photon trajectories that remain outside the black hole. I also present a simpler quadratic approximation that works as well in the middle of the range but not so well at the extremes.

gr-qc↗

arXiv2026

Firewalls, black-hole thermodynamics, and singular solutions of the Tolman-Oppenheimer-Volkoff equation

We investigate thermodynamic equilibrium of a self-gravitating perfect fluid in a spherically symmetric system containing a black hole of mass M by means of the Tolman-Oppenheimer-Volkoff (TOV) equation. At r >> 2M its solutions describe a black-body radiation atmosphere with the Hawking temperature T_BH~1/(8 πM) that is increasingly blueshifted as r approaches 2M. However, there is no horizon at the Schwarzschild radius. Instead, the fluid becomes increasingly hot and dense there, piling up into a "firewall" with the peak temperatures and densities reaching Planck values somewhat below r = 2M. This firewall surrounds a negative point mass residing at r=0, the only singularity of the solution. The entropy of the firewall is comparable to the Bekenstein-Hawking entropy.

gr-qc↗

arXiv2025

Light Black Holes from Light

Alvarez-Dominguez, Garay, Martin-Martinez, and Polo-Gomez have suggested that ``it is not possible to concentrate enough light to precipitate the formation of an event horizon. We argue that the dissipative quantum effects coming from the self-interaction of light (such as vacuum polarization) are enough to prevent any meaningful buildup of energy that could create a black hole in any realistic scenario,'' and ``the dissipation of energy via Schwinger effect alone is enough to prevent the formation of kugelblitze with radii ranging from $10^{-29}$ to $10^8$ m.'' While I agree that it is indeed highly implausible that black holes will form mainly from light in our actual universe, either naturally or by any foreseeable human activity, there are many idealized theoretical processes for forming black holes of any size down to near the Planck length (about $10^{-35}$ m) purely from photons, such as from colliding approximately plane-wave pulses, with only a small fraction of the energy escaping the black hole as scattered light or electron-positron pairs.

hep-th↗

arXiv2024

Graviton Number Radiated During Binary Inspiral

The total number of gravitons emitted during nonrelativistic inspiral of two black holes or other effectively point masses is calculated approximately and found to be remarkably close to (well within 1% of, perhaps within about 0.2% of) the initial orbital angular momentum divided by the spin angular momentum of each graviton ($2\hbar$), although at unit initial eccentricity, $2\hbar$ times the initial graviton number emission per angular momentum emission is $248/(45\sqrt{3}π) \approx 1.012\,811\,600\,479$, almost 1.3% greater than unity.

hep-th↗

arXiv2024

Discrete Orbit Effect Lengthens Merger Times for Inspiraling Binary Black Holes

The inspiral merger time for two black holes captured into a nonrelativistic bound orbit by gravitational radiation emission has been often calculated by a formula of Peters that assumes the adiabatic approximation that the changes per orbit are small. However, initially this is not true for the semimajor axis and period of most of the initially highly eccentric orbits, which change significantly during closest approach and much less elsewhere along the orbit. This effect can make the merger time much longer (using other formulas from Peters that do not assume the adiabatic approximation) than that calculated by the adiabatic formula of Peters.

gr-qc↗

arXiv2024

Inspiral Time Probability Distribution for Two Black Holes Captured by Emitting Gravitational Radiation

If two initially unbound black holes of masses M_1 and M_2, total mass M = M_1 + M_2, reduced mass mu = M_1 M_2/(M_1+M_2), and initial relative velocity v << c(4 mu/M) in otherwise empty space are captured into a bound orbit by emitting gravitational radiation, the inspiral time to coalescence increases monotonically to infinity as the impact parameter b approaches from below the critical impact parameter b_c = [340 pi G^7 M^6 mu/(3 c^5 v^9)]^{1/7} = [(85 pi/384)(4 mu/M)]^{1/7}(2GM/c^2)(v/c)^{-9/7} for capture. Assuming a uniform flux of impinging black holes with b < b_c, the cumulative probability for impact parameters smaller than some value $b$, conditional upon the impact parameter being smaller than $b_c$, is $P = (b/b_c)^2$. Then it is shown that the inspiral time for [Mv^2/(4 mu c^2)]^{2/7} << P < 1 is T = (2 pi GM/v^3) P^{21/4} zeta(3/2,1-P^{7/2}), and closed-form approximate expressions for the inverse function P(T/T_0) with T_0 = 2 pi GM/v^3 are also given.

gr-qc↗

arXiv2022

Can Two Ultrarelativistic Objects Lose Almost All Their Energy to Gravitational Radiation?

In 2007 Pretorius and Khurana did "speculate that at threshold [at a critical impact parameter], all of the kinetic energy of the system [two ultrarelativistic black holes] is converted to gravitational waves, which can be an arbitrarily large fraction of the total energy." However, in 2012 Sperhake, Berti, Cardoso, and Pretorius performed numerical calculations that led them to the contrary conclusion: "An extrapolation of our results to the limit $γ\rightarrow \infty$ suggests that about half of the center-of-mass energy of the system can be emitted in gravitational radiation, while the rest must be converted into rest-mass and spin energy." Here I present arguments against this latter conclusion and in support of the earlier speculation that for sufficiently large $γ$, all but an arbitrarily small fraction of the total energy can be radiated away.

gr-qc↗

arXiv2022

Classicality of Consciousness in Quantum Darwinism

A simple toy model is proposed that would allow conscious perceptions to be either classical (perceptions of objects without large quantum uncertainties or variances) or highly quantum (e.g., having large variances in the perceived position within a single perception), and yet for which plausible quantum states exhibiting Quantum Darwinism would lead to much higher measures for the classical perceptions.

quant-ph↗

arXiv2022

Possibilities for Probabilities

In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for many cosmological purposes. Here a number of possible generalizations of Born's rule are discussed, explaining why they are consistent with the present statistical support for Born's rule in ordinary situations but can help solve various cosmological problems.

hep-th↗

arXiv2022

Critical Gravitational Inspiral of Two Massless Particles

If two ultrarelativistic nonrotating black holes of masses $m_1$ and $m_2$ approach each other with fixed center-of-momentum (COM) total energy $E = \sqrt{s} \gg (m_1+m_2)c^2$ that has a corresponding Schwarzschild radius $R = 2GE/c^4$ much larger than the Schwarzschild radii of the individual black holes, here it is conjectured that at the critical impact parameter $b_c$ between scattering and coalescing into a single black hole, there will be an inspiral of many orbital rotations for $m_1c^2/E \ll 1$ and $m_2c^2/E \ll 1$ before a final black hole forms, during which all of the initial kinetic energy will be radiated away in gravitational waves by the time the individual black holes coalesce and settle down to a stationary state. In the massless limit $m_1 = m_2 = 0$, in which the black holes are replaced by classical massless point particles, it is conjectured that for the critical impact parameter, all of the total energy will be radiated away by the time the two particle worldlines merge and end. One might also conjecture that in the limit of starting with the massless particles having infinite energy in the infinite past with the correct ratio of impact parameter to energy, the spacetime for retarded time before the final worldline merger at zero energy will have a homothetic vector field and hence be self similar. Evidence against these conjectures is also discussed, and if it proves correct, I conjecture that two massless particles can form any number of black holes.

gr-qc↗

arXiv2022

Preserving the Sun from the Cold by a Perfectly Reflecting Dyson Sphere

Some entities, such as humans, survive longest if their environment is neither too hot nor too cold, and the sun is no exception. It is rather obvious that if the sun were enclosed inside a thermally conducting sphere surrounded by a heat bath kept much hotter than the present central temperature of the sun, its nuclear burning would occur faster, so that the sun would last for a shorter time. It is less obvious that if the sun were surrounded by a perfectly reflecting sphere to prevent its radiation from escaping to cold empty space, it could actually last longer. Here I shall show that this is the case for such a sphere at least somewhat larger than the present solar radius. This naively paradoxical result is a consequence of the negative specific heat of many gravitating systems, so as the energy emitted by the sun is reflected back to increase the thermal energy, the sun expands and its central temperature goes down rather than up and reduces the nuclear burning rate, so that the sun can last much longer than five billion years, for a lifetime growing roughly exponentially with the cube root of the radius of the perfectly reflecting sphere.

physics.gen-ph↗

arXiv2021

Does Decoherence Make Observations Classical?

The fact that we rarely directly observe much quantum uncertainty is often attributed to decoherence. However, decoherence does not reduce the quantum uncertainty in the full quantum state. Whether or not it reduces the quantum uncertainties in observations depends on the yet-unknown rules for getting observations (and their measures or `probabilities') from the quantum state. These points are illustrated by a simple toy model with a baseball at 100 miles per hour, which has the Planck momentum.

quant-ph↗

arXiv2021

Photon Boomerang in a Nearly Extreme Kerr Metric

The Kerr rotating black hole metric has unstable photon orbits that orbit around the hole at fixed values of the Boyer-Lindquist coordinate $r$ that depend on the axial angular momentum of the orbit, as well as on the parameters of the hole. For zero orbital axial angular momentum, these orbits cross the rotational axes at a fixed value of $r$ that depends on the mass $M$ and angular momentum $J$ of the black hole. Nonzero angular momentum of the hole causes the photon orbit to rotate so that its direction when crossing the north polar axis changes from one crossing to the next by an angle I shall call $Δϕ$, which depends on the black hole dimensionless rotation parameter $a/M = cJ/(GM^2)$ by an equation involving a complete elliptic integral of the first kind. When the black hole has $a/M \approx 0.994\,341\,179\,923\,26$, which is nearly maximally rotating, a photon sent out in a constant-$r$ direction from the north polar axis at $r \approx 2.423\,776\,210\,035\,73\, GM/c^2$ returns to the north polar axis in precisely the opposite direction (in a frame nonrotating with respect to the distant stars), a photon boomerang.

gr-qc↗

arXiv2020

Possible Superluminal Propagation inside Conscious Beings

The fact that first-person conscious perceptions or sentient experiences have many bits of information strongly suggests that they are produced nonlocally by the effects of many atoms, say by nonlocal quantum operators. If these nonlocal operators act back on the quantum state of the atoms, they could lead to evolution in which signals propagate superluminally, violating the usual causality of local quantum field theory. Although there is not yet any direct evidence that nonlocal operators associated with psycho-physical parallelism act back on the quantum state, it is not totally implausible that this might be the case. In principle the resulting superluminal propagation might be observable by sending signals across brain regions (neural correlates of consciousness) that lead to conscious perceptions.

physics.gen-ph↗

arXiv2019

Ingoing Eddington-Finkelstein Metric of an Evaporating Black Hole

We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.

hep-th↗

arXiv2019

Harmony for 2-Qubit Entanglement

In this Letter we present a new quantity that shows whether two general qubit systems are entangled, which we call harmony. It captures the notion of separability and maximal entanglement. It is also shown that harmony is monogamous for 3-qubit states. Thus, harmony serves as a new entanglement measure. In addition, since it is written as a simple function of the density operator, it is in practice easier to compute than other previously known measures.

quant-ph↗

arXiv2019

No Violation of the Second Law in Extended Black Hole Thermodynamics

Recently a number of papers have claimed that the horizon area - and thus the entropy - of near extremal black holes in anti-de Sitter spacetimes can be reduced by dropping particles into them. In this note we point out that this is a consequence of an underlying assumption that the energy of an infalling particle changes only the internal energy of the black hole, whereas a more physical assumption would be that it changes the enthalpy (mass). In fact, under the latter choice, the second law of extended black hole thermodynamics is no longer violated.

gr-qc↗