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Tyler McMaken

Publications and source records attributed to Tyler McMaken.

15 recordsLinked to original sources
arXiv2026

Black hole singularity is a surface not a point

It is widely repeated in the popular literature and elsewhere that the singularity at the center of a black hole is a point. It is not true. Two observers who free-fall into a spherical black hole along two different angular trajectories at the same time $t$ do not encounter each other at the central singularity; rather, they lose causal contact with each other already well away from the singularity. Counterintuitively, in general relativity two points can be spatially close yet causally distant. The singularity is a surface, not a point. The story for rotating black holes is more complicated, but the same conclusion holds. For a rotating black hole, the singular surface almost certainly resides at its inner horizon, where even the tiniest classical or quantum perturbations ignite the exponential mass inflation instability, precipitating collapse to a spacelike singular surface. There are implications for quantum gravity. We argue that, whatever the ultimate theory of quantum gravity may be, the quantum states of a black hole probably reside at its effectively 2-dimensional singular surface, which coevolves unitarily with, and in thermodynamic equilibrium with, the hot atmosphere of trapped Hawking radiation that the black hole generates within its event horizon.

gr-qc↗
arXiv2025

How physics got its right hand: The origins of chiral conventions in electromagnetism

Why do physicists almost universally take the direction of positive rotation to be counterclockwise, and three-dimensional coordinates to be right-handed? This paper traces the historical development of these chiral conventions, with an emphasis on the physical quantity whose direction became the focal point of this discussion in the mid-1800s, the magnetic field. Though these standards are often reduced to mere mathematical, inconsequential choices, an analysis of the impact of Newton, Maxwell, the London Mathematical Society, and others toward the subject can enhance classroom discussion, not only as a contextual sidebar, but also by emphasizing the influence conventions in physics can have on pedagogy, communication, and scientific advancement.

physics.hist-ph↗
arXiv2025

Towards a Non-singular Paradigm of Black Hole Physics

The study of regular black holes and black hole mimickers as alternatives to standard black holes has recently gained significant attention, driven both by the need to extend general relativity to describe black hole interiors, and by recent advances in observational technologies. Despite considerable progress in this field, significant challenges remain in identifying and characterizing physically well-motivated classes of regular black holes and black hole mimickers. This report provides an overview of these challenges, and outlines some of the promising research directions -- as discussed during a week-long focus programme held at the Institute for Fundamental Physics of the Universe (IFPU) in Trieste from November 11th to 15th, 2024.

gr-qc↗
arXiv2025

Hawking radiation inside a charged, cosmological black hole

We study the effective temperature, as a rate of gravitational redshift, of the Hawking modes perceived by a radially free falling observer at an arbitrary location in a Reissner-Nordström-(anti-)de Sitter [RN(A)dS] spacetime. In particular, the behavior of the modes at the inner horizon, and therein the validity of the strong cosmic censorship conjecture under the effective temperature formalism, has been analyzed across the physically permissible parameter space of the RNdS metric. The modes perceived by observers of both positive and negative specific energies have been taken into consideration. Finally, the behavior of the adiabatic control function has been examined over the position space of the observer to determine the regimes where the effective temperature function yields a Planckian spectrum of thermal radiation.

gr-qc↗
arXiv2024

Backreaction from quantum fluxes at the Kerr inner horizon

Black holes modeled by the Kerr metric are not semiclassically self-consistent at or below the inner horizon. The renormalized stress-energy tensor (RSET) of a scalar quantum field in the Unruh state has been found to diverge at the Kerr inner horizon [arXiv:2203.08502], causing the geometry to backreact in a non-trivial way. In an effort to understand this backreaction, here the inner-horizon RSET is computed for the full physically relevant parameter space of black hole spins $a$ and polar angles $θ$. Then, the backreaction is analyzed using a framework for the dynamical behavior of mass inflation from continued accretion. It is shown that the initial backreaction from the RSET does not evolve the spacetime toward any known regular or extremal configuration, but instead it brings the local interior geometry toward a chaotic, spacelike singularity, classically stable over astrophysical timescales.

gr-qc↗
arXiv2024

Hawking radiation inside a rotating black hole

In semiclassical gravity, the vacuum expectation value ${\langle\hat{N}\rangle}$ of the particle number operator for a quantum field gives rise to the perception of thermal radiation in the vicinity of a black hole. This Hawking effect has been examined only for observers asymptotically far from a Kerr black hole; here we generalize the analysis to various classes of freely falling observers both outside and inside the Kerr event horizon. Of note, we find that the effective temperature of the ${\langle\hat{N}\rangle}$ distribution remains regular for observers at the event horizon but becomes negative and divergent for observers reaching the inner Cauchy horizon. Furthermore, the perception of Hawking radiation varies greatly for different classes of observers, though the spectrum is generally a graybody that decreases in intensity with black hole spin and increases in temperature when looking toward the edges of the black hole shadow.

gr-qc↗
arXiv2023

Existence of Time-like Geodesics in Asymptotically Flat Spacetimes: A Generalized Topological Criterion

This paper examines the issue of the existence and nature of time-like geodesics in asymptotically flat spacetimes and proposes a novel generalized topological criterion for the existence of time-like geodesics. Its validity is proved using theorems such as the Jordan-Brouwer Separation Theorem, the Raychaudhuri Equation, and key elements of Differential Geometry. More specifically, the proof primarily hinges on a closed, simply-connected subset of the spacetime manifold and a continuous map, causing a non-trivial induction on the first homology groups, from the boundary of this subset to a unit circle. The mathematical analysis conclusively affirms the presence of these geodesics, intersecting transversally within the said subset of spacetime. Findings underscore these geodesics' significant implications for the structure of asymptotically flat spacetimes, including stability, and hypothetical existence of wormholes. The generalized topological criterion also has implications on the problem of obstructions for the existence of Lorentzian metrics, and Einstein's Constraint Equations. Future research should extend this topological criterion to other classes of spacetimes, including those with non-trivial topologies or non-zero cosmological constants. Also, the criterion's application to study complex dynamical systems, such as gravitational waves or rotating black holes, could offer significant insights.

gr-qc↗
arXiv2023

Unification of the four forces in the Spin(11,1) geometric algebra

SO(10), or equivalently its covering group Spin(10), is a well-known promising grand unified group that contains the standard-model group. The spinors of the group Spin($N$) of rotations in $N$ spacetime dimensions are indexed by a bitcode with $[N/2]$ bits. Fermions in Spin(10) are described by five bits $yzrgb$, consisting of two weak bits $y$ and $z$, and three colour bits $r$, $g$, $b$. If a sixth bit $t$ is added, necessary to accommodate a time dimension, then the enlarged Spin(11,1) algebra contains the standard-model and Dirac algebras as commuting subalgebras, unifying the four forces. The minimal symmetry breaking chain that breaks Spin(11,1) to the standard model is unique, proceeding via the Pati-Salam group. The minimal Higgs sector is similarly unique, consisting of the dimension~66 adjoint representation of Spin(11,1); in effect, the scalar Higgs sector matches the vector gauge sector. Although the unified algebra is that of Spin(11,1), the persistence of the electroweak Higgs field after grand symmetry breaking suggests that the gauge group before grand symmetry breaking is Spin(10,1), not the full group Spin(11,1). The running of coupling parameters predicts that the standard model should unify to the Pati-Salam group Spin(4)$_w \times$Spin(6)$_c$ at $10^{12}\,$GeV, and thence to Spin(10,1) at $10^{15}\,$GeV. The grand Higgs field breaks $t$-symmetry, can drive cosmological inflation, and generates a large Majorana mass for the right-handed neutrino by flipping its $t$-bit. The electroweak Higgs field breaks $y$-symmetry, and generates masses for fermions by flipping their $y$-bit.

physics.gen-ph↗
arXiv2023

Semiclassical instability of inner-extremal regular black holes

The construction of black hole spacetimes that are regular (singularity-free) is plagued by the "mass inflation" instability, a classical perturbation instability induced by the surface gravity at the inner horizon and characterized by exponentially diverging stress-energy there. Recently, a class of "inner-extremal" regular black holes was proposed that possesses a vanishing inner-horizon surface gravity and therefore avoids mass inflation, while still maintaining a horizon separation and a non-zero outer-horizon surface gravity. However, when semiclassical effects are taken into account, it is found that an inner-horizon instability remains for generic inner-extremal regular black holes formed from collapse. This semiclassical divergence is analyzed from the perspective of both the effective Hawking temperature and the renormalized stress-energy tensor, and its origin and genericity are examined in detail.

gr-qc↗
arXiv2023

Pancakification and negative Hawking temperatures

Vacuum models of charged or spinning black holes possess two horizons, the inner of which has the oft-overlooked property that gravitational tidal forces initially spaghettifying a freely falling observer will eventually change signs and flatten the observer like a pancake. Inner horizons also induce a classical blueshift instability known as mass inflation, and a number of recent studies have found that inner horizons exhibit even stronger quantum singular behavior. In this essay we explore the quantum effect of Hawking radiation, which in the presence of compressive tidal forces seems to predict negative temperatures. By analyzing the interaction of quantum fields with black hole geometries, we can come to a closer semiclassical understanding of what really happens near a black hole's inner horizon.

gr-qc↗
arXiv2023

Hawking radiation inside a charged black hole

Here we analyze the Hawking radiation detected by an inertial observer in an arbitrary position in a Reissner-Nordström spacetime, with special emphasis on the asymptotic behavior of the Hawking spectrum as an observer approaches the inner or outer horizon. Two different methods are used to analyze the Hawking flux: first, we calculate an effective temperature quantifying the rate of exponential redshift experienced by an observer from an emitter's vacuum modes, which reproduces the Hawking effect provided the redshift is sufficiently adiabatic. Second, we compute the full Bogoliubov graybody spectrum observed in the three regimes where the wave equation can be solved analytically (at infinity and at the outer and inner horizons). We find that for an observer at the event horizon, the effective Hawking temperature is finite and becomes negative when $(Q/M)^2>8/9$, while at the inner horizon, the effective temperature is always negative and infinite in every direction the observer looks, coinciding with an ultraviolet-divergent spectrum.

gr-qc↗
arXiv2022

Renormalization of $\langleϕ^2\rangle$ at the inner horizon of rotating, accreting black holes

Classically, the inner horizon of a perturbed, rotating black hole undergoes an instability known as mass inflation, wherein the spacetime curvature diverges as a result of hyper-relativistic crossing streams of ingoing and outgoing radiation. The generic outcome of this instability is currently believed to be a strong, spacelike singularity, potentially alongside a weak, null singularity surviving at late times. However, the quantum back-reaction in this regime has yet to be fully calculated for a realistic black hole spacetime. Here we consider a massless quantized scalar field $ϕ$ over the inflationary Kasner spacetime, a recently developed model for the inner horizon geometry of a rotating, accreting black hole. With this spacetime, we use numerical adiabatic regularization to calculate $\langleϕ^2\rangle_\text{ren}$, the renormalized coincidence limit of the two-point correlation function, as a pointer to the behavior of the quantum stress-energy tensor. $\langleϕ^2\rangle_\text{ren}$ is generically found to be nonzero near the inner horizon, divergent where the curvature classically diverges, and larger for smaller black hole spins or accretion rates.

gr-qc↗
arXiv2022

Notes on primordial black hole origin for thermal gamma-ray bursts

Recently, an alleged plausible astrophysical scenario was proposed for the production of observed thermal gamma-ray bursts, via Hawking radiation emitted from a primordial black hole (PBH) freely falling into a more massive black hole. Here the implausibility of that scenario is demonstrated, and the key flaws in that paper's calculations and assumptions are elucidated through a discussion of some common misconceptions concerning black holes and general relativity. In particular, the predicted radiance observed from Earth is found to be orders of magnitude lower than what any instrument could detect, and the PBH-BH merger signature would be completely overwhelmed by the background Hawking signature from free PBHs.

gr-qc↗
arXiv2021

Geometry near the inner horizon of a rotating, accreting black hole

Here we present a novel classical model to describe the near-inner horizon geometry of a rotating, accreting black hole. The model assumes spacetime is homogeneous and is sourced by radial streams of a collisionless, null fluid, and it predicts that the standard Poisson-Israel mass inflation phenomenon will be interrupted by a Kasner-like collapse toward a spacelike singularity. Such a model is shown to be valid at the inner horizon of astrophysically realistic black holes through comparison to the conformally-separable model, which provides a natural connection of the Kerr metric to a self-similar, accreting spacetime. We then analyze the behavior of null geodesics in our model, connecting them to the Kerr metric in order to answer the practical question of what an infalling observer approaching the inner horizon might see.

gr-qc↗