This textbook offers a mathematically rigorous overview of the theory of relativity, emphasizing the transition from classical to relativistic mechanics.

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 arbitrarily far from equilibrium and refers to finite changes that occur due to physical processes at the horizon. The second law is now a 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.

These lecture notes develop polariton fluids of light as programmable simulators of quantum fields on tailored curved spacetimes, with emphasis on acoustic horizons and the Hawking effect. After introducing exciton-polariton physics in semiconductor microcavities, we detail the theoretical tools to study the mean field and the quantum hydrodynamics of this driven-dissipative quantum system. We derive the mapping to relativistic field theories and cast horizon physics as a pseudounitary stationary scattering problem. We present the Gaussian optics circuit that describes observables and fixes detection weights for the horizon modes in near- and far-field measurements. We provide a practical experimental toolkit (phase-imprinted flows, coherent pump-probe spectroscopy, balanced and homodyne detection) and a step-by-step workflow to extract amplification, quadrature squeezing, and entanglement among correlations. Finally, we discuss the potential of this platform to investigate open questions in quantum field theory in curved spacetime, such as near horizon effects and quasinormal modes, as well as other phenomena universal to rotating geometries, from rotational superradiance to dynamical instabilities. We further outline the interplay between rotational superradiance and the Hawking effect, proposing to spatially resolve measurements as a roadmap for ‘dumb hole spectroscopy’ and the study of entanglement dynamics in curved spacetimes.

Using LARES-2, LAGEOS and GRACE satellites, researchers measured Earth’s frame-dragging with unprecedented precision, strongly confirming general relativity, constraining alternative gravity theories, and improving measurements of Earth’s tides.

Analogue gravity is a research programme that explores analogues of general relativistic gravitational fields within other physical systems, particularly but not exclusively in condensed matter systems, with the aim of gaining new insights into related problems. Analogue models of gravity boast a long and distinguished history, dating back to the early years of general relativity. This review article delves into the history, aims, results, and future prospects of various analogue models. We begin by presenting a particularly simple example of an analogue model, then traverse the rich history and complex array of models discussed in the literature. The last decade has witnessed significant and sustained advances in analogue gravity, resulting in hundreds of published articles, workshops, and books. The future of the analogue gravity programme looks promising, with rapid technological advances on the experimental front and the potential for analogue models to inspire innovative approaches to the problem of quantum gravity on the theoretical front. Most of all, these recent years have seen the rise of an unprecedented collaboration and interplay between different communities that we believe will set a new standard for interdisciplinary research in the years to come.

Hyperboloidal foliations which extend to future null infinity are advantageous in extracting gravitation radiation and monitoring the approach to horizon formation. A simple hyperboloidal foliation of the Kerr-Newman family of charged, spinning black hole spacetimes is presented. Its potential application to the simulation of the full range of perturbations of sub-extremal Kerr-Newman black holes is outlined.

We provide some guidance and examples to clear up common misconceptions about special relativity. These misconceptions often come from trying to express the truths of special relativity in Newtonian t...

Springer's editorial policies for journals underpin our commitment to editorial independence and supporting research excellence.

One of the greatest mysteries of modern physics, the "black hole information paradox," might have finally found an elegant solution, and the answer could also reveal the origins of the mass of fundamental particles.

Gaia has recently revealed a population of over 20 compact objects in wide astrometric binaries, while LIGO-Virgo-KAGRA (LVK) have observed around 100 compact object binaries as gravitational-wave (GW) mergers. Despite belonging to different systems, the compact objects discovered by both Gaia and the LVK follow a multimodal mass distribution, with a global maximum at neutron star (NS) masses ( ∼ 1 $\sim 1$ – 2 M ⊙ $2\,M_{\odot }$ ) and a secondary local maximum at black hole (BH) masses ∼ 10 M ⊙ $\sim 10\,M_{\odot }$ . However, the relative dearth of objects, or “mass gap,” between these modes is more pronounced among the wide binaries observed by Gaia compared to the GW population, with 9 − 6 + 10 % $9^{+10}_{-6}\%$ of GW component masses falling between 2.5– 5 M ⊙ $5\,M_{\odot }$ compared to ≲ 5 % $\lesssim 5\%$ of Gaia compact objects. We explore whether this discrepancy can be explained by the natal kicks received by low-mass BHs. GW progenitor binaries may be more likely to survive natal kicks, because the newborn BH has a more massive companion and/or is in a tighter binary than Gaia progenitor binaries. We compare the survival probabilities of Gaia and GW progenitor binaries as a function of natal kick strength and pre-supernova binary parameters, and map out the parameter space and kick strength required to disrupt the progenitor binaries leading to low-mass BHs in Gaia systems more frequently than those in GW systems.

Gupta was among the first to attempt the quantization of Einstein’s nonlinear theory of gravity. He had an independent program to quantize gravity in a manner akin to electromagnetism, which spanned at least two decades. He adopted the flat-space views of Rosen and Papapetrou and built his theory around these ideas. Although he was well known for his work in quantum electrodynamics, little is known about his work in quantum gravity. For that reason, in this paper, we try to present a historical overview of his research program.

This paper offers a historical overview of the origins and enduring significance of gravitational particle creation, a groundbreaking discovery first formulated in Leonard Parker’s 1966 doctoral thesi...

Gravitational waves emitted from the coalescence of neutron star binaries open a new window to probe matter and fundamental physics in unexplored, extreme regimes. To extract information about the sup...

This book is a compact introduction to geometrised Newtonian (Newton-Cartan) gravity. It’s designed with exercises to master advanced concepts.

The first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This White Paper outlines the challenges and gains expected ...

We provide a short introduction to “Lorentzian metric spaces” i.e., spacetimes defined solely in terms of the two-point Lorentzian distance. As noted in previous work, this structure is essentially un...

We present a detailed analysis that may significantly impact understanding the relationship between structure formation in the late-epoch Universe and dark energy as described by the Friedmann-Lemaîtr...

Arrays of precisely-timed millisecond pulsars are used to search for gravitational waves with periods of months to decades. Gravitational waves affect the path of radio pulses propagating from a pulsa...

This book highlights the state of the art of machine learning applied to the science of gravitational waves and encapsulates the immense amount of finding

Pune: Theoretical physicist Naresh Dadhich, who co-founded Inter-University Centre for Astronomy and Astrophysics (IUCAA) in Pune along with eminent a.

This book documents progress in the TianQin project ranging from scientific research to technological innovation and data analysis

October 2025 Virtual Infinity Seminar by István Rácz (Wigner Research Centre for Physics)

Recently, it was shown that type D black holes, encompassed in the large Plebanśki–Demiański (PD) family, exhibit a wide class of algebraically general generalizations via the application of Ehlers and Harrison transformations. In this work, we first discuss some mathematical details behind the composition of such transformations, and next, we introduce a qualitative picture of the most general type I generalization of the PD family, dubbed “Enhanced Plebanśki–Demiański” spacetime. We provide the exact form of the solution in the original PD coordinates, obtained via the simultaneous action of an Ehlers and a Harrison transformation on the vacuum PD geometry. In order to make the physics more transparent, we explicitly construct a rotating and accelerating black hole which further has NUT parameter and electric charges, both of them entering, not only the event horizon, but the Rindler horizon as well. This solution is directly obtained in the “physical” coordinates recently proposed by Podolský and Vrátny. Finally, a pedagogical appendix is thoughtfully included, providing readers with a user-friendly step-by-step guide to the Ernst formalism, in an attempt to address and resolve various minor inconsistencies frequently appearing in the relevant literature.