Rudeep Gaur’s research while affiliated with Victoria University of Wellington and other places

There has recently been some considerable interest expressed in a highly speculative model of black-hole evolution—allegedly by a postulated direct coupling between black holes and cosmological expansion independent of accretion or mergers. We wish to make several cautionary comments in this regard—at least three exact solutions corresponding to black holes embedded in a Friedmann-Lemaître-Robertson-Walker background are known (Kottler, McVittie, Kerr–de Sitter), and they show no hint of this claimed effect, thereby implying that this claimed effect (if it exists at all) is certainly nowhere near ubiquitous.

We bring the Kerr--Newman spacetime into the Bondi--Sachs gauge by means of zero angular momentum, null geodesics. We compute the memory effect produced at the black hole horizon by a transient gravitational shock wave, which from future null infinity is seen as a Bondi-Metzner-Sachs supertranslation. This results in a change of the supertransformation charges at infinity between the spacetime geometries defined by the black hole before, and after, the shockwave scattering. For an extremal Kerr--Newman black hole, we give the complementary description of this process in the near-horizon limit, as seen by an observer hovering over the horizon. In this limit, we compute the supertranformation charges and compare them to those calculated at null infinity. We analyze the effect of these transformations on the electromagnetic gauge field and explore the self-interaction between this and the angular momentum of the black hole.

A bstract Black and white holes play remarkably contrasting roles in general relativity versus observational astrophysics. While there is observational evidence for the existence of compact objects that are “cold, dark, and heavy”, which thereby are natural candidates for black holes, the theoretically viable time-reversed variants — the “white holes” — have nowhere near the same level of observational support. Herein we shall explore the theoretical possibility that the connection between black and white holes is much more intimate than commonly appreciated. We shall first construct “horizon penetrating” coordinate systems that differ from the standard curvature coordinates only in a small near-horizon region, thereby emphasizing that ultimately the distinction between black and white horizons depends only on near-horizon physics. We shall then construct an explicit model for a “black-to-white transition” where all of the nontrivial physics is confined to a compact region of spacetime — a finite-duration finite-thickness, (in principle arbitrarily small), region straddling the naïve horizon. Moreover we shall show that it is possible to arrange the “black-to-white transition” to have zero action — so that it will not be subject to destructive interference in the Feynman path integral. This then raises the very intriguing possibility that astrophysical black holes might be interpretable in terms of a quantum superposition of black and white horizons — a “gray” horizon.

The various “defect wormholes” developed by Klinkhamer have recently attracted considerable attention—especially in view of the fact that the simplest example, the so-called “vacuum defect wormhole”, was claimed to be an everywhere-vacuum everywhere-Ricci-flat exact solution to the Einstein equations. This claim has been conclusively refuted by Feng, and in the current article, we take a deeper look at exactly what goes wrong. The central issue is this: Although Klinkhamer’s specific representation of the metric gab is smooth (C∞), his inverse metric gab is not even everywhere continuous (C0), being undefined at the wormhole throat. This situation implies that one should very carefully investigate curvature tensors at the throat using the Israel–Lanczos–Sen thin-shell formalism. Doing so reveals the presence of a delta-function energy-condition-violating thin shell of matter at the wormhole throat. The “defect wormholes” are thus revealed to be quite ordinary “cut-and-paste” thin-shell wormholes, but represented in a coordinate system that is unfortunately pathological at exactly the same place that all the interesting physics occurs. To help clarify the situation, we shall focus on the behavior of suitable coordinate invariants—the Ricci scalar, the eigenvalues of the mixed Rab Ricci tensor, and the eigenvalues of the mixed Rabcd Riemann tensor.

The various "defect wormholes" developed by Klinkhamer have recently attracted considerable attention -- especially in view of the fact that the simplest example, the so-called "vacuum defect wormhole", was claimed to be an everywhere-vacuum everywhere-Ricci-flat exact solution to the Einstein equations. This claim has been conclusively refuted by Feng, and in the current article we take a deeper look at exactly what goes wrong. The central issue is this: Although Klinkhamer's specific representation of the metric g_{ab} is smooth (C^\infty) his inverse metric g^{ab} is not even everywhere continuous (C^0), being undefined at the wormhole throat. This situation implies that one should very carefully investigate curvature tensors at the throat using the Israel--Lanczos--Sen thin-shell formalism. Doing so reveals the presence of a delta-function energy-condition-violating thin shell of matter at the wormhole throat. The "defect wormholes" are thus revealed to be quite ordinary "cut-and-paste" thin-shell wormholes, but represented in a coordinate system which is unfortunately pathological at exactly the same place that all the interesting physics occurs.

There has recently been some considerable interest expressed in a highly speculative model of black hole evolution -- allegedly by a postulated direct coupling between black holes and cosmological expansion independently of accretion or mergers. We wish to make several cautionary comments in this regard -- at least three exact solutions corresponding to black holes embedded in a FLRW background are known, (Kottler, McVittie, Kerr-de~Sitter), and they show no hint of this claimed effect -- thereby implying that this claimed effect (if it exists at all) is certainly nowhere near ubiquitous.

Black and white holes play remarkably contrasting roles in general relativity versus observational astrophysics. While there is overwhelming observational evidence for the existence of compact objects that are "cold, dark, and heavy", which thereby are natural candidates for black holes, the theoretically viable time-reversed variants -- the "white holes" -- have nowhere near the same level of observational support. Herein we shall explore the possibility that the connection between black and white holes is much more intimate than commonly appreciated. We shall first construct "horizon penetrating" coordinate systems that differ from the standard curvature coordinates only in a small near-horizon region, thereby emphasizing that ultimately the distinction between black and white horizons depends only on near-horizon physics. We shall then construct an explicit model for a "black-to-white transition" where all of the nontrivial physics is confined to a compact region of spacetime -- a finite-duration finite-thickness, (in principle arbitrarily small), region straddling the naive horizon. Moreover we shall show that it is possible to arrange the "black-to-white transition" to have zero action -- so that it will not be subject to destructive interference in the Feynman path integral. This then raises the very intriguing possibility that astrophysical black holes might be interpratable in terms of a quantum superposition of black and white horizons.

Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) “at rest”, while “space” is expanding. But this is merely a specific coordinate choice; and it is important to realise that for certain purposes other, (sometimes radically , different) coordinate choices might also prove useful and informative, but without changing the underlying physics. Specifically, herein we shall consider the k = 0 spatially flat FLRW cosmology but in Painlevé-Gullstrand coordinates — these coordinates are very explicitly not co-moving: “space” is now no longer expanding, although the distance between galaxies is still certainly increasing. Working in these Painlevé-Gullstrand coordinates provides an alternate viewpoint on standard cosmology, and the symmetries thereof, and also makes it somewhat easier to handle cosmological horizons. With a longer view, we hope that investigating these Painlevé-Gullstrand coordinates might eventually provide a better framework for understanding large deviations from idealized FLRW spacetimes. We illustrate these issues with a careful look at the Kottler and McVittie spacetimes.

Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) "at rest", while "space" is expanding. But this is merely a specific coordinate choice; and it is important to realise that for certain purposes other, (sometimes radically different) coordinate choices might also prove useful and informative, but without changing the underlying physics. Specifically, herein we shall consider the k=0 spatially flat FLRW cosmology but in Painleve-Gullstrand coordinates -- these coordinates are very explicitly not co-moving: "space" is now no longer expanding, although the distance between galaxies is still certainly increasing. Working in these Painleve-Gullstrand coordinates provides an alternate viewpoint on standard cosmology, and the symmetries thereof, and also makes it somewhat easier to handle cosmological horizons. With a longer view, we hope that investigating these Painleve-Gullstrand coordinates might eventually provide a better framework for understanding large deviations from idealized FLRW spacetimes. We illustrate these issues with a careful look at the Kottler and McVittie spacetimes.