A Study of the Fluctuations in the Apparent Horizon Location

-using Curvature Flow Method

-using Apr091998.2 T90 Data

-1 hole, 57 cubed Cartesian grid

Apr091998.2 T90 Data: Levels 1 - 50

The data shows an approximate error in area of 6%.

Level	Time	Area
1	0.00	113.01403689812673
2	12.5	110.82643196290003
3	25.0	109.76607257911137
4	37.5	109.84143989070462
5	50.0	113.31567896961667
6	62.5	116.36199852655126
7	75.0	117.08274703682969
8	87.5	115.83818059217722
9	100.0	113.7541756136812
10	112.5	111.99486632303379
11	237.5	111.41140407355647
12	250.0	112.77285180817867
13	262.5	114.7050735788803
14	275.0	115.71703897458197
15	287.5	115.41580845398124
16	300.0	114.28838979543096
17	400.0	113.10525550581096
18	412.5	112.588882158296
19	425.0	113.01652444784278
20	437.,5	113.97653830704616
21	450.0	114.72295264947419
22	462.5	114.81314624479283
23	475.0	114.32830421063878
24	487.5	113.66718527496359
25	500.0	113.26359034067842
26	512.5	113.33403816573446
27	525.0	113.76344695230138
28	537.5	114.216447369612
29	550.0	114.401580176358
30		114.24210952208975
31		113.8927436522826
32		113.61380650209742
33		113.57507548715517
34		113.76661629081877
35		114.00296741630068
36		114.14545272544302
37		114.14065728244438
38		114.01752414479448
39		113.85045996099362
40		113.76012274011306
41		113.8524081349813
42		114.05621461001887
43		114.25397337667215
44	537.5	114.32196087111545
45	550.0	114.52594386386208
46	562.5	114.73258192226156
47	575.0	115.28818364352389
48	587.5	115.67851697895206
49	600.0	116.85018281293711
50	612.5	117.83087921586515

Note: Area in this table is measure 3, using line elements. Where time is missing, the time

was not saved during the run. The time jump between levels 10, 11 and 16,17 is arbitrary since the

run was restarted after levels 10 and 16.

The following images plot a slice of the apparent horizons surface in the polar plane using Cartesian coordinates.

Note: bh50&bh1 indicates levels 50 and 1 are plotted together to show how the surface changed.

All plots are at an outgoing convergence of approximately 10^-5; therefore, the uncertainty in

the location of the apparent horizon is on the order of 10^-5. All plots are at the final time for

each level.

Analysis:

bh50&bh1 - the two surfaces visually do not coincide
bh50&bh25 - the two surfaces visually do not coincide
bh50&bh45 - the two surfaces visually do not coincide

bh1&bh25 - the two surfaces visually coincide
bh25&bh45 - the two surfaces visually coincide