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Abhay Ashtekar

Publications and source records attributed to Abhay Ashtekar.

At least 19 recordsLinked to original sources
arXiv2026

Thermodynamics of dynamical black holes beyond perturbation theory

The close similarities of the three laws of black hole mechanics, discovered by Bardeen, Carter and Hawking, with the laws of thermodynamics led to the identification of a multiple of the area of the event horizon with entropy. However, developments over the past two decades have shown that this paradigm has some important limitations, especially because of the teleological nature of event horizons. After a brief review of these limitations, we will show that they can be overcome using quasi-local horizons. Specifically, the new first law applies to black holes in general relativity that can be \emph{arbitrarily far from equilibrium} and refers to \emph{finite} changes that occur due to \emph{physical processes} at the horizon. The second law is now a \emph{quantitative} statement that relates the change in the area of a dynamical horizon segment due to fluxes of energy falling into the black hole. Together, they lead one to identify black hole entropy with the area of marginally trapped surfaces in quasi-local horizons, generalizing recent perturbative findings that it should be identified not with the area of the event horizon but with the area of a marginally trapped surface inside it.

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arXiv2025

Thermodynamics of Black Holes, far from Equilibrium

As in thermodynamics, the celebrated first law of black hole mechanics relates infinitesimal changes in the properties of nearby equilibrium states of black holes (without reference to any physical process that causes the transition). Using dynamical horizon segments (DHSs), we extend the first law to encompass black holes that can be arbitrarily far from equilibrium. It now refers to \emph{finite} changes that occur due to \emph{physical processes}. This extension, together with the generalized second law on DHSs \cite{Ashtekar:2003hk}, naturally lead one to identify entropy of dynamical BHs with the area DHSs.

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arXiv2025

Dynamical Horizon Segments and Spacetime Isometries

Given a space-time $(\mathscr{M}, g_{ab})$ admitting a dynamical horizon segment (DHS) $\mathscr{H}$, we show that there are stringent constraints on the Killing fields $\xi^a$ that $g_{ab}$ can admit in a neighborhood of $\mathscr{H}$: Generically, $\xi^a$ can only be a rotational Killing field which, furthermore, leaves each marginally trapped 2-sphere cross-section $\mathcal{S}$ of $\mathscr{H}$ invariant. Finally, if $\xi^a$ happens to be hypersurface orthogonal near $\mathscr{H}$, then, not only the angular momentum but also all spin multipoles vanish on every $\mathcal{S}$; the entire spin structure of these DHSs is indistinguishable from that of spherically symmetric DHSs!

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arXiv2025

Quasi-Local Black Hole Horizons: Recent Advances

While the early literature on black holes focused on event horizons, subsequently it was realized that their teleological nature makes them unsuitable for many physical applications both in classical and quantum gravity. Therefore, over the past two decades, event horizons have been steadily replaced by quasi-local horizons which do not suffer from teleology. In numerical simulations event horizons can be located as an `after thought' only after the entire space-time has been constructed. By contrast, quasi-local horizons naturally emerge in the course of these simulations, providing powerful gauge-invariant tools to extract physics from the numerical outputs. They also lead to interesting results in mathematical GR, providing unforeseen insights. For example, for event horizons we only have a qualitative result that their area cannot decrease, while for quasi-local horizons the increase in the area during a dynamical phase is quantitatively related to local physical processes at the horizon. In binary black hole mergers, there are interesting correlations between observables associated with quasi-local horizons and those defined at future null infinity. Finally, the quantum Hawking process is naturally described as formation and evaporation of a quasi-local horizon. This review focuses on the dynamical aspects of quasi-local horizons in classical general relativity, emphasizing recent results and ongoing research.

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arXiv2025

Black Hole Evaporation in Loop Quantum Gravity

The conference \emph{Black Holes Inside and Out} marked the 50th anniversary of Hawking's seminal paper on black hole radiance. It was clear already from Hawking's analysis that a proper quantum gravity theory would be essential for a more complete understanding of the evaporation process. This task was undertaken in Loop Quantum Gravity (LQG) two decades ago and by now the literature on the subject is quite rich. The goal of this contribution is to summarize a mainstream perspective that has emerged. The intended audience is the broader gravitational physics community, rather than quantum gravity experts. Therefore, the emphasis is on conceptual issues, especially on the key features that distinguish the LQG approach, and on concrete results that underlie the paradigm that has emerged. This is \emph{not} meant to be an exhaustive review. Rather, it is a broad-brush stroke portrait of the present status. Further details can be found in the references listed.

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arXiv2024

Black Holes Inside and Out 2024: visions for the future of black hole physics

The gravitational physics landscape is evolving rapidly, driven by our ability to study strong-field regions, in particular black holes. Black Holes Inside and Out gathered world experts to discuss the status of the field and prospects ahead. We hope that the ideas and perspectives are a source of inspiration. Structure: Black Hole Evaporation - 50 Years by William Unruh The Stability Problem for Extremal Black Holes by Mihalis Dafermos The Entropy of Black Holes by Robert M. Wald The Non-linear Regime of Gravity by Luis Lehner Black Holes Galore in D > 4 by Roberto Emparan Same as Ever: Looking for (In)variants in the Black Holes Landscape by Carlos A. R. Herdeiro Black Holes, Cauchy Horizons, and Mass Inflation by Matt Visser The Backreaction Problem for Black Holes in Semiclassical Gravity by Adrian del Rio Black Holes Beyond General Relativity by Enrico Barausse and Jutta Kunz Black Holes as Laboratories: Searching for Ultralight Fields by Richard Brito Primordial Black Holes from Inflation by Misao Sasaki Tests of General Relativity with Future Detectors by Emanuele Berti Black Holes as Laboratories: Tests of General Relativity by Ruth Gregory and Samaya Nissanke Simulating Black Hole Imposters by Frans Pretorius Black Hole Spectroscopy: Status Report by Gregorio Carullo VLBI as a Precision Strong Gravity Instrument by Paul Tiede Testing the nature of compact objects and the black hole paradigm by Mariafelicia De Laurentis and Paolo Pani Some Thoughts about Black Holes in Asymptotic Safety by Alessia Platania Black Hole Evaporation in Loop Quantum Gravity by Abhay Ashtekar How the Black Hole Puzzles are Resolved in String Theory by Samir D. Mathur Quantum Black Holes: From Regularization to Information Paradoxes by Niayesh Afshordi and Stefano Liberati

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arXiv2024

The Operational Meaning of Total Energy of Isolated Systems in General Relativity

We present thought experiments to measure the Arnowitt-Deser-Misner and Bondi-Sachs energy of isolated systems in general relativity. The expression of the Bondi-Sachs energy used in the protocol is likely to have other applications. In particular, it is well-suited to to be promoted to an operator in non-perturbative loop quantum gravity.

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arXiv2024

Null Infinity as a Weakly Isolated Horizon

Null infinity arises as a boundary of the Penrose conformal completion of an asymptotically flat physical space-time. We first note that null infinity is a weakly isolated horizon (WIH), and then show that its familiar properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs is very different from that extracted at null infinity. We show that these differences can be directly traced back to the fact that null infinity is a WIH in the conformal completion rather than the physical space-time. In particular, the BMS group at null infinity stems from the symmetry group of WIHs. In a companion paper, we obtain fluxes and charges associated with symmetries associated with both null infinity and black hole (and cosmological) horizons using a new Hamiltonian framework. The fact that is there is a single mathematical framework underlying these different situations paves the way to explore the relation between horizon dynamics in the strong field region and waveforms at infinity. It should also be useful in the analysis of black hole evaporation in quantum gravity.

hep-th↗
arXiv2024

Null Infinity and Horizons: A New Approach to Fluxes and Charges

We introduce a Hamiltonian framework tailored to degrees of freedom (DOF) of field theories that reside in suitable 3-dimensional open regions, and then apply it to the gravitational DOF of general relativity. Specifically, these DOF now refer to open regions of null infinity, and of black hole (and cosmological) horizons representing equilibrium situations. At null infinity the new Hamiltonian framework yields the well-known BMS fluxes and charges. By contrast, all fluxes vanish identically at black hole (and cosmological) horizons just as one would physically expect. In a companion paper we showed that, somewhat surprisingly, the geometry and symmetries of these two physical configurations descend from a common framework. This paper reinforces that theme: Very different physics emerges in the two cases from a common Hamiltonian framework because of the difference in the nature of degrees of freedom. Finally, we compare and contrast this Hamiltonian approach with those available in the literature.

hep-th↗
arXiv2024

Horizons and Null Infinity: A Fugue in 4 voices

Black hole horizons in equilibrium and null infinity of asymptotically flat space-times are null 3-manifolds but have very different physical connotations. We first show that they share a large number of geometric properties, making them both weakly isolated horizons. We then use this new unified perspective to unravel the origin of the drastic differences in the physics they contain. Interestingly, the themes are woven together in a manner reminiscent of voices in a fugue.

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arXiv2024

Unified Treatment of Null and Spatial Infinity III: Asymptotically Minkowski Space-times

The Spi framework provides a 4-dimensional approach to investigate the asymptotic properties of gravitational fields as one recedes from isolated systems in any space-like direction, without reference to a Cauchy surface. It is well suited to unify descriptions at null and spatial infinity because $\mathscr{I}$ arises as the null cone of $i^\circ$. The goal of this work is to complete this task by introducing a natural extension of the asymptotic conditions at null and spatial infinity, by 'gluing' the two descriptions appropriately. Space-times satisfying these conditions are asymptotically flat in both regimes and thus represent isolated gravitating systems. They will be said to be Asymptotically Minkowskian at $i^\circ$. We show that in these space-times the Spi group $\mathfrak{S}$ as well as the BMS group $\mathcal{B}$ naturally reduce to a single Poincaré group, denoted by $\mathfrak{p}_{i^\circ}$ to highlight the fact that it arises from the gluing procedure at $i^\circ$. The asymptotic conditions are sufficiently weak to allow for the possibility that the Newman-Penrose component $Ψ^\circ_1$ diverges in the distant past along $\mathscr{I}^+$. This can occur in astrophysical sources that are not asymptotically stationary in the past, e.g. in scattering situations. Nonetheless, as we show in the companion paper, the energy momentum and angular momentum defined at $i^\circ$ equals the sum of that defined at a cross-section $S$ of $\mathscr{I}^+$ and corresponding flux across $\mathscr{I}^+$ to the past of $S$, when the quantities refer to the preferred Poincaré subgroup $\mathfrak{p}_{i^\circ}$.

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arXiv2023

Unified Treatment of null and Spatial Infinity IV: Angular Momentum at Null and Spatial Infinity

In a companion paper we introduced the notion of asymptotically Minkowski spacetimes. These space-times are asymptotically flat at both null and spatial infinity, and furthermore there is a harmonious matching of limits of certain fields as one approaches $i^\circ$ in null and space-like directions. These matching conditions are quite weak but suffice to reduce the asymptotic symmetry group to a Poincaré group $\mathfrak{p}_{i^\circ}$. Restriction of $\mathfrak{p}_{i^\circ}$ to future null infinity $\mathscr{I}^{+}$ yields the canonical Poincaré subgroup $\mathfrak{p}^{\rm bms}_{i^\circ}$ of the BMS group $\mathfrak{B}$ selected in the companion paper and its restriction to spatial infinity $i^\circ$ gives the canonical subgroup $\mathfrak{p}^{\rm spi}_{i^\circ}$ of the Spi group $\mathfrak{S}$ there. As a result, one can meaningfully compare angular momentum that has been defined at $i^\circ$ using $\mathfrak{p}^{\rm spi}_{i^\circ}$ with that defined on $\mathscr{I}^{+}$ using $\mathfrak{p}^{\rm bms}_{i^\circ}$. We show that the angular momentum charge at $i^\circ$ equals the sum of the angular momentum charge at any 2-sphere cross-section $S$ of $\mathscr{I}^{+}$ and the total flux of angular momentum radiated across the portion of $\mathscr{I}^{+}$ to the past of $S$. In general the balance law holds only when angular momentum refers to ${\rm SO(3)}$ subgroups of the Poincaré group $\mathfrak{p}_{i^\circ}$.

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arXiv2023

Black Hole Horizons and their Mechanics

Black holes are often characterized by event horizons, following the literature that laid the mathematical foundations of the subject in the 1970s. However black hole event horizons have two fundamental conceptual limitations. First, they are defined only in space-times that admit a future conformal boundary. Second, they are teleological; their formation and growth is not determined by local physics but depends on what could happen in the distant future. Therefore, event horizons have not played much of a role in the recent theoretical advances that were sparked by discoveries of the LIGO-virgo collaborations. This article focuses on quasi-local horizons that have been used instead. Laws governing them -- mechanics of quasi-local horizons -- generalize those that were first found using event horizons. These results, obtained over the last two decades or so, have provided much insight into dynamical predictions of general relativity in the fully nonlinear regime. The article summarizes the deep and multi-faceted interplay between geometry and physics that has emerged. Conceptually, quasi-local horizons also play a key role in the discussion of the quantum evaporation of black holes. However, due to space limitations, this application is only briefly discussed in Section 6.

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arXiv2023

Regular black holes from Loop Quantum Gravity

There is rich literature on regular black holes from loop quantum gravity (LQG), where quantum geometry effects resolve the singularity, leading to a quantum extension of the classical space-time. As we will see, the mechanism that resolves the singularity can also trigger conceptually undesirable features that can be subtle and are often uncovered only after a detailed examination. Therefore, the quantization scheme has to be chosen rather astutely. We illustrate the new physics that emerges first in the context of the eternal black hole represented by the Kruskal space-time in classical general relativity, then in dynamical situations involving gravitational collapse, and finally, during the Hawking evaporation process. The emphasis is on novel conceptual features associated with the causal structure, trapping and anti-trapping horizons and boundedness of invariants associated with curvature and matter. This Chapter is not intended to be an exhaustive account of all LQG results on non-singular black holes. Rather, we have selected a few main-stream thrusts to anchor the discussion, and provided references where further details as well as discussions of related developments can be found. In the spirit of this Volume, the goal is to present a bird's eye view that is accessible to a broad audience.

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arXiv2022

Exploring quantum geometry created by quantum matter

Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized. The goal of this investigation is to probe the `Coulombic' aspects of quantum geometry that are governed entirely by matter sources. Since there are no gravitational waves in 3 dimensions, 3-d gravity coupled to matter provides an ideal arena for this task. Our analysis will reveal novel aspects of quantum gravity that bring out limitations of classical and semi-classical theories in unforeseen regimes: non-linearities of general relativity can magnify small quantum fluctuations in the matter sector to large effects in the gravitational sector. Finally, this analysis leads to thought experiments that bring out rather starkly why understanding of the nature of physical reality depends sensitively on the theoretical lens with which it is probed. As theories becomes richer, new scales emerge, triggering novel effects that could not be imagined before. The model provides a concise realization of this well-known chain.

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arXiv2022

Probing cosmological singularities with quantum fields: Open and closed FLRW universes

It was recently pointed out that linear quantum fields $\hat ϕ(x)$ can be meaningfully propagated across the big bang (and the big crunch) singularities of spatially flat Friedmann, Lemaître, Robertson, Walker (FLRW) universes \cite{ADLS2021}. Recall that $\hat ϕ(x)$, as well as renormalized observables $\langle\hat ϕ(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$, are distribution-valued already in Minkowskian quantum field theories. It was shown that they can be extended as well-defined distributions even when these space-times are enlarged to include the big-bang (or the big crunch). We generalize these results to spatially closed and open FLRW models, showing that this `tameness' of cosmological singularities is not an artifact of the technical simplifications due to spatial flatness. Our analysis also provides explicit expressions of $\langle\hat ϕ(x) \hat ϕ(x') \rangle_{ren}$, $\langle\hat ϕ(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$ in closed and open universes for minimally coupled massless scalar fields and discuss the ambiguities in the definition of $\langle \hat T_{ab}(x)\rangle_{ren}$ at the big-bang. While the technical expressions are more complicated than in the spatially flat case, there is also an unexpected conceptual simplification: the infrared divergence \cite{fp} is now absent because, in effect, the spatial curvature provides a natural cutoff. Finally, we further clarify the sense in which quantum field theory can continue to be well defined even though the extended space-time is not globally hyperbolic because of the singularity, and suggest directions for further work.

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arXiv2022

Non-Expanding horizons: Multipoles and the Symmetry Group

It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non-expanding horizons (NEHs). In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature. We then show that the symmetry group $\mathfrak{G}$ of NEHs is a 1-dimensional extension of the BMS group $\mathfrak{B}$. These symmetries are used in a companion paper to define charges and fluxes on NHEs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that $\mathcal{I}^\pm$ of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that $\mathcal{I}^\pm$ have a small additional structure that reduces $\mathfrak{G}$ to the BMS group $\mathfrak{B}$, and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at $\mathcal{I}^+$.

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