Schwarzschild metric - 2025 ACF Winter

Question

Birkhoff’s theorem guarantees the uniqueness of this metric. For 10 points each:

[10m] Name this solution to the Einstein field equations that describes space around a static, uncharged, spherically symmetric mass.

ANSWER: Schwarzschild metric [or Schwarzschild solution; or Schwarzschild black hole; or Schwarzschild vacuum]

[10e] The Schwarzschild metric predicts this feature for a black hole at the Schwarzschild radius. These features are a boundary beyond which light cannot escape.

ANSWER: event horizons [prompt on horizons]

[10h] The Schwarzschild radius is an example of one of these locations where the metric is undefined, but do not reflect a physical divergence. These features can be avoided by using transformations like ones named after tortoises or Kruskal.

ANSWER: coordinate singularity [accept removable singularity; prompt on singularity; reject “gravitational singularity”; reject “curvature singularity”]

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Summary


California	Main	Y	5	20.00	100%	80%	20%
Canada	Main	Y	6	13.33	100%	33%	0%
Florida	Main	Y	12	15.00	100%	50%	0%
Great Lakes	Main	Y	6	13.33	100%	17%	17%
Lower Mid-Atlantic	Main	Y	7	14.29	71%	71%	0%
Midwest	Main	Y	8	15.00	100%	50%	0%
North	Main	Y	11	10.00	100%	0%	0%
Northeast	Main	Y	5	10.00	100%	0%	0%
Overflow	Main	Y	4	12.50	100%	25%	0%
Upstate NY	Main	Y	8	13.75	100%	25%	13%
2025 ACF Nationals	2025-08-09	Y	14	17.14	100%	36%	36%
2024 ARCADIA at UC Berkeley	04/19/2025	Y	4	12.50	100%	25%	0%

Data


Berkeley B	Berkeley A	10	10	0	20
Berkeley D	Stanford B	10	10	0	20
Stanford A	Berkeley E	10	10	0	20
Berkeley C	Stanford C	10	10	10	30
UCSC	Berkeley F	0	10	0	10
UCSD Vices and Virtues	UCI	10	10	0	20
UCLA A	Claremont Scripps	0	10	0	10
UCLA B	Claremont Pitzer	0	10	0	10
UCLA C	UCSD Two Running Violet V Forms	0	10	0	10
Toronto A	McGill B	10	10	0	20
McMaster C	Toronto E	10	10	0	20
McMaster A	Ottawa	0	10	0	10
Toronto I	Queen's A	0	10	0	10
Toronto J	Toronto G	10	10	0	20
Waterloo	Toronto D	0	10	0	10
UCSD What Hath God Wrought	UCSB	0	10	0	10
Western Ontario	Guelph A	0	10	0	10
Carleton	Guelph B	10	10	0	20
McGill C	Queen's B	0	10	0	10
Toronto H	Toronto C	0	10	0	10
Toronto B	Toronto K	10	10	0	20
Toronto F	Toronto Metropolitan	10	10	0	20
USC	UCLA D	10	10	0	20
FSU	ERAU A	0	10	0	10
UF D	Melbourne A	0	10	0	10
UF A	FIU	0	10	10	20
UCF B	UF E	0	10	0	10
USF	ERAU B	0	10	0	10
UCF A	UF B	10	10	0	20
MSU B	CWRU C	10	10	0	20
CWRU A	CWRU B	10	10	0	20
Pitt A	MSU A	10	10	0	20
OSU A	OSU B	10	10	0	20
OSU C	OSU D	10	10	0	20
Pitt C	CWRU D	0	0	0	0
Clemson A	James Madison	0	10	0	10
South Carolina A	Tennessee A	10	10	0	20
Tennessee B	Virginia B	0	10	0	10
NC State	Virginia Tech B	10	10	0	20
Liberty A	Liberty C	0	10	0	10
Tusculum	South Carolina B	10	10	0	20
Virginia A	Clemson B	10	10	0	20
Roanoke	Virginia Tech A	0	10	0	10
George Mason A	Catholic University	0	10	0	10
George Mason C	George Washington B	0	10	0	10
George Washington A	Georgetown B	0	10	0	10
Johns Hopkins A	VCU A	0	10	0	10
Maryland A	George Mason B	0	10	0	10
Maryland B	Johns Hopkins B	0	10	0	10
Georgetown A	Maryland C	0	10	0	10
NYU A	Penn A	0	10	0	10
Maryland D	NYU B	0	10	0	10
Penn B	Johns Hopkins C	0	10	0	10
Notre Dame E	UMBC A	0	10	0	10
Missouri A	WashU B	0	10	0	10
WashU A	Missouri B	10	10	0	20
WashU C	William Woods	0	10	0	10
Truman State	WashU D	0	10	0	10
Lehigh B	Columbia A	0	10	0	10
Swarthmore A	Columbia B	0	10	0	10
Columbia C	Princeton A	0	10	0	10
Lehigh A	Rowan A	0	10	0	10
Rutgers B	Rutgers C	0	10	0	10
Alabama A	UAB A	0	10	0	10
Alabama B	Georgia Tech B	0	10	0	10
Vanderbilt A	Georgia Tech C	0	10	0	10
Imperial A	Birmingham A	10	10	0	20
Cambridge C	Bristol A	0	10	10	20
Imperial B	City St George's A	10	10	10	30
Cambridge B	Durham A	10	10	10	30
Durham B	Southampton B	0	10	0	10
Cambridge A	Edinburgh A	0	10	0	10
Imperial C	Cambridge D	0	10	0	10
LSE A	Manchester A	10	10	0	20
Manchester B	Bristol B	0	10	0	10
Oxford A	Southampton A	0	10	0	10
Sheffield B	Oxford B	0	10	10	20
Lancaster A	Sheffield C	10	10	10	30
Sheffield A	Warwick A	0	10	0	10
Warwick B	Edinburgh B	0	10	0	10
Auburn A	Mississippi State A	10	10	0	20
Bruin A	Auburn B	0	10	0	10
Georgia Tech D	Huntsville B	0	10	0	10
Sewanee A	Huntsville A	0	10	0	10
Georgia Tech A	Vanderbilt B	10	10	10	30
Binghamton A	RIT A	0	10	0	10
RIT B	Cornell-DII	10	10	0	20
ESF	Rochester	0	10	0	10
Syracuse	Binghamton B	0	10	0	10
Kenyon B	Kenyon A	0	0	0	0