Explore general relativity, black holes, and gravitation by subject. Each volume connects physical ideas, mathematical reasoning, and research applications.
Special relativity, spacetime geometry, Einstein’s equations, exact solutions, causal structure, and black-hole mechanics.
Provide the operational and physical preparation needed to understand gravitation, from Newtonian dynamics and special relativity through classical matter, waves, thermodynamics, and bounded quantum bridges.
Develop the invariant geometric language of relativistic spacetime, from manifolds and tensors through curvature, geodesics, frames, hypersurfaces, bundles, and global tools.
Present the conceptual and local dynamical heart of Einstein gravity as a coherent path from equivalence and measurement to curvature, field equations, matter coupling, focusing, and tested weak-field predictions.
Develops exact metric-field solutions, their coordinate domains and invariants, and the checks and methods used to relate spacetime families.
Develop the stable causal and global framework needed to define predictability, horizons, infinity, singularities, topology, and censorship before theorem-specific proofs or dated verdicts are considered.
Build a precise geometric and mechanical account of black holes by connecting global and quasi-local horizon definitions to equilibrium anatomy, conserved charges, classification, extremality, and classical energy extraction.
Relativistic matter, black-hole response, interacting bodies, gravitational collapse, and the radiation they produce.
Develop relativistic material equations, closure relations, stellar equilibrium and response, compact-star physics, collapse microphysics, matter-rich mergers, and horizonless compact alternatives.
Develop linear and controlled weakly nonlinear fields on black-hole backgrounds from gauge-invariant equations through causal response, spectra, stability, superradiance, absorption, tidal response, and near-extremal dynamics.
Organize interacting compact-body dynamics across post-Newtonian, post-Minkowskian, amplitude, worldline, self-force, effective-one-body, spin, tidal, radiation-reaction, and strong-encounter descriptions, with controlled overlaps and invariant validation.
Develop finite-amplitude formation and evolution of horizons and black holes, including collapse, interiors, nonlinear instabilities, mergers, remnants, and dynamical tests of censorship.
Develop source-independent gravitational-radiation theory, asymptotic observables, generation and propagation, fluxes and memory, signal representations, waveform construction, and quantitative standards for waveform accuracy.
Formulate Einstein’s equations, establish their mathematical properties, and solve them with checked computational methods.
Develop equivalent continuum formulations of Einstein gravity, making gauge, data, constraints, hyperbolicity, boundaries, canonical structure, and charge machinery explicit before discretization.
Provide theorem-first treatments of Einstein PDE, regularity, geometric analysis, global existence, stability, rigidity, inequalities, singularity formation, inextendibility, censorship, and inverse problems.
Develop symbolic and numerical realizations of relativistic systems, from reproducible workflows and discretization through spacetime evolution, matter, extraction, synthetic observations, reduced models, verification, validation, and computational evidence.
Black-hole populations and environments, gravitational-wave observations, and the dynamics and history of the Universe.
Explain black-hole formation and demographics, stellar and gaseous environments, accretion, radiation, jets, electromagnetic observables, imaging, and astrophysical source interpretation.
Develop the complete detector-to-inference chain for gravitational-wave astronomy: instruments, calibration, noise, searches, parameter estimation, catalogs, populations, selection effects, multimessenger association, and open-data reproducibility.
Develop relativistic cosmological dynamics, observables, perturbations, horizons, structure, primordial black holes, cosmological gravitational waves, and baseline inference with explicit model and evidence boundaries.
Construct consistent extensions of general relativity and test gravity across laboratory, astrophysical, and cosmological regimes.
Develop alternative and effective gravitational theories through their field content, dynamical consistency, recovery of general relativity, solution branches, and theory-specific compact-object, radiative, and cosmological predictions.
Develop operational test design, phenomenological deviation frameworks, null tests, comparative likelihoods, systematic-error analysis, cross-regime inference, and empirical conclusions about gravity.
Quantum fields on curved backgrounds, thermodynamics, backreaction, information, quantum gravity, strings, and holography.
Develop nongravitational quantum fields on prescribed curved backgrounds through states, representations, local observables, detectors, renormalization, particle creation, Unruh physics, and fixed-background Hawking flux.
Develop the semiclassical Einstein equation and its validity, stress-tensor backreaction, response and fluctuations, black-hole thermodynamics, generalized laws, evaporation dynamics, and semiclassical horizon physics.
Formulate the black-hole information problem precisely and develop fine-grained entropy, interior consistency, replica gravity, quantum extremal surfaces, islands, reconstruction, operational questions, and comparative recovery criteria.
Develop common conceptual problems, low-energy quantum general relativity, and non-string candidate approaches to quantum spacetime with comparative evidence and operational interfaces.
Develop gravity-facing string and holographic black-hole physics through supergravity and branes, protected entropy counting, AdS black holes, thermal gravity, near-AdS2 systems, reconstruction, and black-hole-specific holographic interfaces.
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