seminars:anal
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seminars:anal [2025/11/17 15:58] xxu |
seminars:anal [2025/12/05 15:14] (current) xxu |
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| - | **//Abstract//**: Consider the metric in $\cal{R}^4$ given by $ds^2=f(r)dt^2 − 1/f(r)dr^2 − r^2dg^2$, where $g$ is the standard Riemannian metric in $\cal{R}^2$, $f(r) = \phi(r)(r − r-0)$, where $\phi$ is a continuous, differentiable, positive function on $\cal{R}$. We will construct the Penrose diagram (the compactified manifold) for the given metric via coordinate changes and compactification. We will then discuss extensions to topological Penrose Diagrams and metric functions with an arbitrary number of roots, if time permits. | + | **//Abstract//**: Consider the metric in $\mathbb{R}^4$ given by $ds^2=f(r)dt^2 − 1/f(r)dr^2 − r^2dg^2$, where $g$ is the standard Riemannian metric in $\mathbb{R}^2$, $f(r) = \phi(r)(r − r_0)$, where $\phi$ is a continuous, differentiable, positive function on $\mathbb{R}$. We will construct the Penrose diagram (the compactified manifold) for the given metric via coordinate changes and compactification. We will then discuss extensions to topological Penrose Diagrams and metric functions with an arbitrary number of roots, if time permits. |
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| * **December 3rd, Wednesday ** (4:00-5:00pm)\\ \\ | * **December 3rd, Wednesday ** (4:00-5:00pm)\\ \\ | ||
| - | **//Speaker//**: Chad Nelson (Binghamton University) \\ | + | **//Speaker//**: Job interview \\ |
| - | **//Topic//**: TBD | + | **//Topic//**: |
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| <WRAP box 80%> **//Abstract//**: | <WRAP box 80%> **//Abstract//**: | ||
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| * **January 28th, Wednesday ** (4-5pm)\\ | * **January 28th, Wednesday ** (4-5pm)\\ | ||
| - | \\ **//Speaker //**: TBD | + | \\ **//Speaker //**: Chad Nelson (Binghamton University) |
| \\ **//Topic//**: | \\ **//Topic//**: | ||
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seminars/anal.1763413124.txt · Last modified: 2025/11/17 15:58 by xxu