### 2009

Seahra, S. S.

Gravitational waves from braneworld black holes Journal Article

In: Lect. Notes Phys., vol. 769, pp. 347–386, 2009.

@article{Seahra:2009zz,

title = {Gravitational waves from braneworld black holes},

author = {S. S. Seahra},

editor = {Eleftherios Papantonopoulos},

url = {https://sanjeev.seahra.ca/wp-content/uploads/2022/01/black_string.pdf},

doi = {10.1007/978-3-540-88460-6_9},

year = {2009},

date = {2009-01-01},

urldate = {2009-01-01},

journal = {Lect. Notes Phys.},

volume = {769},

pages = {347--386},

abstract = {In these lecture notes, we present the black string model of a braneworld black hole and analyze its perturbations. We develop the perturbation formalism for Randall-Sundrum model from first principles and discuss the weak field limit of the model in the solar system. We derive explicit equations of motion for the axial and spherical gravitational waves in the black string background. These are solved numerically in various scenarios, and the characteristic late-time signal from a black string is obtained. We find that if one waits long enough after some transient event, the signal from the string will be a superposition of nearly monochromatic waves with frequencies corresponding to the masses of the Kaluza Klein modes of the model. We estimate the amplitude of the spherical component of these modes when they are excited by a point particle orbiting the string.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

In these lecture notes, we present the black string model of a braneworld black hole and analyze its perturbations. We develop the perturbation formalism for Randall-Sundrum model from first principles and discuss the weak field limit of the model in the solar system. We derive explicit equations of motion for the axial and spherical gravitational waves in the black string background. These are solved numerically in various scenarios, and the characteristic late-time signal from a black string is obtained. We find that if one waits long enough after some transient event, the signal from the string will be a superposition of nearly monochromatic waves with frequencies corresponding to the masses of the Kaluza Klein modes of the model. We estimate the amplitude of the spherical component of these modes when they are excited by a point particle orbiting the string.

### 2006

Seahra, Sanjeev

An introduction to black holes Unpublished

2006.

@unpublished{nokey,

title = {An introduction to black holes},

author = {Sanjeev Seahra},

url = {https://sanjeev.seahra.ca/wp-content/uploads/2022/01/black_holes.pdf},

year = {2006},

date = {2006-02-06},

urldate = {2006-02-06},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

### 2002

Seahra, Sanjeev S.

The Classical and Quantum Mechanics of Systems with Constraints Unpublished

2002.

@unpublished{nokey,

title = {The Classical and Quantum Mechanics of Systems with Constraints},

author = {Sanjeev S. Seahra},

url = {https://sanjeev.seahra.ca/wp-content/uploads/2022/01/constrained_quantization.pdf},

year = {2002},

date = {2002-05-23},

urldate = {2002-05-23},

abstract = {In these notes, we discuss the classical and quantum mechanics of finite dimensional mechanical systems subject to constraints. We review Dirac’s classical formalism of dealing with such problems and motivate the definition of objects such as singular and non-singular action principles, first- and second-class constraints, and the Dirac bracket. We show how systems with first-class constraints can be considered to be systems with gauge freedom. A consistent quantization scheme using Dirac brackets is described for classical systems with only second class constraints. Two different quantization schemes for systems with first-class constraints are presented: Dirac and canonical quantization. Systems invariant under reparameterizations of the time coordinate are considered and we show that they are gauge systems with first-class constraints. We conclude by studying an example of a reparameterization invariant system: a test particle in general relativity.},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

In these notes, we discuss the classical and quantum mechanics of finite dimensional mechanical systems subject to constraints. We review Dirac’s classical formalism of dealing with such problems and motivate the definition of objects such as singular and non-singular action principles, first- and second-class constraints, and the Dirac bracket. We show how systems with first-class constraints can be considered to be systems with gauge freedom. A consistent quantization scheme using Dirac brackets is described for classical systems with only second class constraints. Two different quantization schemes for systems with first-class constraints are presented: Dirac and canonical quantization. Systems invariant under reparameterizations of the time coordinate are considered and we show that they are gauge systems with first-class constraints. We conclude by studying an example of a reparameterization invariant system: a test particle in general relativity.

### 2000

Seahra, Sanjeev S.

Path Integrals in Quantum Field Theory Unpublished

2000.

@unpublished{nokey,

title = {Path Integrals in Quantum Field Theory},

author = {Sanjeev S. Seahra},

url = {https://sanjeev.seahra.ca/wp-content/uploads/2022/01/path_integrals.pdf},

year = {2000},

date = {2000-05-11},

urldate = {2000-05-11},

abstract = {We discuss the path integral formulation of quantum mechanics and use it to derive the S matrix in terms of Feynman diagrams. We generalize to quantum field theory, and derive the generating functional Z[J] and n-point correlation functions for free scalar field theory. We develop the generating functional for self-interacting fields and discuss φ^4 and φ^3 theory.},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

We discuss the path integral formulation of quantum mechanics and use it to derive the S matrix in terms of Feynman diagrams. We generalize to quantum field theory, and derive the generating functional Z[J] and n-point correlation functions for free scalar field theory. We develop the generating functional for self-interacting fields and discuss φ^4 and φ^3 theory.

Seahra, Sanjeev S.

Beyond Flat Space Quantum Field Theory Unpublished

2000.

@unpublished{nokey,

title = {Beyond Flat Space Quantum Field Theory},

author = {Sanjeev S. Seahra},

url = {https://sanjeev.seahra.ca/wp-content/uploads/2022/01/quantum_curved.pdf},

year = {2000},

date = {2000-05-11},

abstract = {We examine the quantum field theory of scalar field in non-Minkowski spacetimes. We first develop a model of a uniformly accelerating particle detector and demonstrate that it will detect a thermal spectrum of particles when the field is in an “empty” state (according to inertial observers). We then develop a formalism for relating field theories in different coordinate systems (Bogolubov transformations), and apply it to compare comoving observers in Minkowski and Rindler spacetimes. Rindler observers are found to see a hot bath of particles in the Minkowski vacuum, which confirms the particle detector result. The temperature is found to be proportional to the proper acceleration of comoving Rindler observers. This is generalized to 2D black hole spacetimes, where the Minkowski frame is related to Kruskal coordinates and the Rindler frame is related to conventional (t, r) coordinates. We determine that when the field is in the Kruskal (Hartle-Hawking) vacuum, conventional observers will conclude that the black hole acts as a blackbody of temperature κ/2πk (k is Boltzmann’s constant). We examine this result in the context of static particle detectors and thermal Green’s functions derived from the 4D Euclidean continuation of the Schwarzschild manifold. Finally, we give a semi-qualitative 2D account of the emission of scalar particles from a ball of matter collapsing into a black hole (the Hawking effect).},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

We examine the quantum field theory of scalar field in non-Minkowski spacetimes. We first develop a model of a uniformly accelerating particle detector and demonstrate that it will detect a thermal spectrum of particles when the field is in an “empty” state (according to inertial observers). We then develop a formalism for relating field theories in different coordinate systems (Bogolubov transformations), and apply it to compare comoving observers in Minkowski and Rindler spacetimes. Rindler observers are found to see a hot bath of particles in the Minkowski vacuum, which confirms the particle detector result. The temperature is found to be proportional to the proper acceleration of comoving Rindler observers. This is generalized to 2D black hole spacetimes, where the Minkowski frame is related to Kruskal coordinates and the Rindler frame is related to conventional (t, r) coordinates. We determine that when the field is in the Kruskal (Hartle-Hawking) vacuum, conventional observers will conclude that the black hole acts as a blackbody of temperature κ/2πk (k is Boltzmann’s constant). We examine this result in the context of static particle detectors and thermal Green’s functions derived from the 4D Euclidean continuation of the Schwarzschild manifold. Finally, we give a semi-qualitative 2D account of the emission of scalar particles from a ball of matter collapsing into a black hole (the Hawking effect).