Spacetime and Geometry: An Introduction to General Relativity

Published on Jan 1, 2003
Sean M. Carroll56
Estimated H-index: 56
(California Institute of Technology)
Sources
Abstract
Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity for advanced undergraduates and graduate students. It introduces modern techniques and an accessible and lively writing style to what can often be a formal and intimidating subject. Readers are led from physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. Subtle points are illuminated throughout the text by careful and entertaining exposition. A straightforward and lucid approach, balancing mathematical rigor and physical insight, are hallmarks of this important text.
Download
馃摉 Papers frequently viewed together
2004
1 Author (Eric Poisson)
References0
Newest
Cited By1210
Newest
#1Mark T. LuskH-Index: 23
#2Andrew A. VoitivH-Index: 2
Last. Mark E. SiemensH-Index: 22
view all 4 authors...
We present an analytical means of quantifying the fractional accumulation of geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a Poincar\'e Sphere is endowed with a Supplementary Product Space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of geometric phase across a single lens as a function of initial state and lens posit...
#1Justin C. Feng (University of Lisbon)
#2Sumanta Chakraborty (IACS: Indian Association for the Cultivation of Science)H-Index: 30
The Weiss variation of the Einstein-Hilbert action with an appropriate boundary term has been studied for general boundary surfaces; the boundary surfaces can be spacelike, timelike, or null. To achieve this we introduce an auxiliary reference connection and find that the resulting Weiss variation yields the Einstein equations as expected, with additional boundary contributions. Among these boundary contributions, we obtain the dynamical variable and the associated conjugate momentum, irrespecti...
#1Abdul Jawad (CUI: COMSATS Institute of Information Technology)H-Index: 26
#2Shahid Chaudhary (CUI: COMSATS Institute of Information Technology)H-Index: 2
Last. Iarley P. Lobo (UFPB: Federal University of Para铆ba)H-Index: 14
view all 3 authors...
Abstract null null The study of greybody factor helps us to understand the quantum nature of the black hole. Gravitational potentials and bounds on the greybody factors for some well known black holes are developed and we investigate the influence of Born鈥揑nfeld and massive gravity parameters on them. It is observed that greybody factor bounds depend on the shape of effective potential. For higher values of effective potential, it becomes difficult for the waves to transmit and hence reduces the...
Source
Self-gravitating non-topological solitons whose potential admits multiple vacua are promising candidates for exotic compact objects. Such objects can arise in several extensions of the Standard Model and could be produced in the early Universe. In this work, we focus on objects made from complex scalars (gravitating Q-balls/soliton boson stars), deriving analytic solutions in spherical symmetry and comparing them with fully numerical ones. In the high-compactness limit we find that these objects...
#1Karen Yagdjian (University of Texas at Austin)H-Index: 18
#2Anahit Galstian (University of Texas at Austin)H-Index: 9
We present the fundamental solutions for the spin-1/2 fields propagating in the spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.
Source
In this article I first introduce and cover preliminaries of point particle mechanics in a Randers-Finsler spacetime, and describe formulation of different equivalent spacetimes via Jacobi-Maupertuis and Eisenhart lift. Then I proceed to discuss Randers-Finsler geometry in the context of gravitational optics, and the formulation of a Riemannian optical metric as an equivalent spacetime.
In this article, we study further applications of the Schwarzschild-Finsler-Randers (SFR) model which was introduced in a previous work. In this model, we investigate curvatures and the generalized Kretschmann invariant which plays a crucial role for singularities. In addition, the derived path equations are used for the gravitational redshift of the SFR-model and these are compared with the GR model. Finally, we get some results for different values of parameters of the generalized photonsphere...
Source
#1Anirudh Pradhan (GLA University)H-Index: 41
#2Archana Dixit (GLA University)H-Index: 4
鈥odel is based on Tsallis holographic dark energy with observational constraints in flat FLRW spacetime geometry with higher derivative theory of gravity.鈥he model exhibits a smooth transition from deceleration to acceleration.鈥e have solved the field equations by applying energy conservation-law in non-interacting case.鈥e have obtained the various cosmological parameters viz. Hubble parameter, deceleration parameter, jerk, snap, lerk and max-out.鈥onstraining on Hubble parameters H(z) by th...
Source
Abstract null null In this paper, locally rotationally symmetric Bianchi type-I cosmological models in null null null null f null ( null R null , null 蠒 null ) null null null null theory of gravity have been investigated, where null null null R null null null and null null null 蠒 null null null are Ricci scalar and scalar potential function, respectively. Some exact solutions pertaining to the dark energy and the cosmic expansion have been found by implementing the power law model null null null...
Source
Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g. state of neurons) and slow-changing trainable variables (e.g. weights and biases). We show that the non-equilibrium dynamics of trainable variables can be described by the Madelung equations, if the number of neurons is fixed, and by the Schrodinger equation, if the learning system is capable of adjusting its own parameters such as the number of neurons, step s...
This website uses cookies.
We use cookies to improve your online experience. By continuing to use our website we assume you agree to the placement of these cookies.
To learn more, you can find in our Privacy Policy.